Causal structure in the presence of sectorial constraints, with application to the quantum switch

Abstract

Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a system can suffer sectorial constraints, that is, restrictions on the orthogonal subspaces of its Hilbert space that may be mapped to one another. Our framework (a) proves that a number of different intuitions about causal relations turn out to be equivalent; (b) shows that quantum causal structures in the presence of sectorial constraints can be represented with a directed graph; and (c) defines a fine-graining of the causal structure in which the individual sectors of a system bear causal relations. As an example, we apply our framework to purported photonic implementations of the quantum switch to show that while their coarse-grained causal structure is cyclic, their fine-grained causal structure is acyclic. We therefore conclude that these experiments realize indefinite causal order only in a weak sense. Notably, this is the first argument to this effect that is not rooted in the assumption that the causal relata must be localized in spacetime.

References in corpus (51)

• Decoherence Free Subspaces for Quantum Computation
• Noiseless Quantum Codes
• Quantum Computers and Dissipation
• Reference frames, superselection rules, and quantum information
• Quantum correlations with no causal order
• Preserving coherence in quantum computation by pairing quantum bits
• Quantum computations without definite causal structure
• Theoretical framework for quantum networks
• Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
• Transforming quantum operations: quantum supermaps
• The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
• Experimental Superposition of Orders of Quantum Gates
• Computational advantage from quantum-controlled ordering of gates
• Experimental Verification of an Indefinite Causal Order
• Quantum causal modelling
• Perfect discrimination of no-signalling channels via quantum superposition of causal structures
• Indefinite Causal Order in a Quantum Switch
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Quantum common causes and quantum causal models
• Witnessing causal nonseparability
• Bell's Theorem for Temporal Order
• Quantum Refrigeration with Indefinite Causal Order
• Quantum Shannon theory with superpositions of trajectories
• The simplest causal inequalities and their violation
• Quantum computation with programmable connections between gates
• Communication through coherent control of quantum channels
• Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
• Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios
• Resource theories of communication
• A purification postulate for quantum mechanics with indefinite causal order
• A graph-separation theorem for quantum causal models
• Cyclic Quantum Causal Models
• The space of logically consistent classical processes without causal order
• Quantum gravity computers: On the theory of computation with indefinite causal structure
• Two-way communication with a single quantum particle
• Experiments on quantum causality
• Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders
• Experimental entanglement of temporal order
• Experimental two-way communication with one photon
• Causal Boxes: Quantum Information-Processing Systems Closed under Composition
• A generalization of Schur-Weyl duality with applications in quantum estimation
• Routed quantum circuits
• Causal and compositional structure of unitary transformations
• Indefinite Causal Orders from Superpositions in Time
• Existence of processes violating causal inequalities on time-delocalised subsystems
• Universal control of quantum processes using sector-preserving channels
• Quantum switch in the gravity of Earth
• Carrying an arbitrarily large amount of information using a single quantum particle
• AB effect and Aharonov-Susskind charge non-superselection
• Operational interpretation of the vacuum and process matrices for identical particles
• The Combinatorics of Causality

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• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
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• Quantum metrology in the finite-sample regime
• Existence of processes violating causal inequalities on time-delocalised subsystems
• Security of differential phase shift QKD from relativistic principles
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Fundamental limits for realising quantum processes in spacetime
• Gravitational quantum switch on a superposition of spherical shells
• Equivalence Principle in Classical and Quantum Gravity
• Indefinite causal order and quantum coordinates
• Quantum Supermaps are Characterized by Locality
• Consistent circuits for indefinite causal order
• Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Toward an Experimental Device-Independent Verification of Indefinite Causal Order
• What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks
• Knot invariants and indefinite causal order